1. Field of Invention
The present invention relates generally to magnetic fields and particularly to fields for containing charged particles and ionized gases such as plasmas used in nuclear fusion reactors.
2. Background Art
Plasma containment by magnetic fields has followed two main pathways in an attempt to successfully sustain a nuclear fusion reaction. The open-ended type, such as the magnetic mirror, have suffered from large plasma losses through the mirror ends. The toroidal type, such as the tokamak, have suffered losses as a result of the magnetic field lines exhibiting a convex rather than a concave curvature with respect to the particles traveling in the torus.
The magnetic mirror effect is the result of a plasma particle moving along the field lines toward a region of increasing field strength, the mirror, and being repelled by a repulsive force reacting on its circular current. The simple mirror is achieved by a pair of coils which have fields of similar polarity. The combined field forms two magnetic mirrors between which a plasma can be trapped. The major plasma losses occur with particles having a travel path that is oriented along the field line directly through the center of either coil, and thereby through the center of the mirrors. Several different configurations of mirror-type magnetic fields have been proposed to address the end loss problem. Mirror cells have been linked together to form roughly a toroidal structure to eliminate the mirror ends by connecting them to the next adjacent mirror (U.S. Pat. No. 3,170,841 and 3,728,217). Simple mirrors suffer the same problem of convex field lines as toroidal structures. If the current in one of the coils of a simple mirror is reversed, a magnetic cusp is formed. This configuration has, in addition to the usual mirrors, a spindle-cusp mirror extending 360 degrees in azimuth. This changed field line curvature to concave, but resulted in additional plasma losses at the cusp plane between the two mirrors. Cusp mirrors have been proposed that were linked into toroidal shapes (U.S. Pat. No. 3,668,067), with a variety of mechanisms that were meant to reduce the losses from the respective spindle-cusp planes (U.S. Pat. No. 3,461,033). Although the cusp type magnetic field is more stable due to the concave condition, the existence of a magnetic field zero point at the center of the structure results in the impairment of a single-particle confinement. The magnetic moment is no longer an adiabatic invariant of the system, and a particle passing through the zero field point will have a motion which bears no relationship to the motion prior to its passage through the zero field point. Annular mirrors were proposed to define an annular magnetic field region having a non-zero minimum field and still retained the flux line curvature that is convex from the central plasma surface (U.S. Pat. 3,369,140). The simple mirror structure can be altered by the addition of four Ioffe bars carrying current in alternate directions. The plasma is distorted into an asymmetric shape, and finds itself in an absolute magnetic well, with the field strength increasing in every direction. Any structure with a minimum B field, or a magnetic well, will have added stability, as plasma will tend to drift to regions of lower field strength. A further refinement of this configuration is to combine the Ioffe bars and the main mirror coils into a single winding. The winding has the shape of a seam on a baseball and is called a baseball coil. Enhancements of this type of cusp magnetic mirror arrangements include the multiple seam baseball coil (U.S. Pat. No. 3,491,318) and the Yin-Yang coil (U.S. Pat. No. 3,582,849). These coils had the added benefits of approximating three-dimensional symmetry, but in all cases plasma losses occur at points and lines of symmetry within the structures. Both baseball and Yin-Yang coils have been used as tandem mirrors to minimize losses from the ends of a solenoid. In these cases the two types of coils act as plugs to help confine the plasma in the central solenoid. A polyhedral arrangement of multiple cusp magnets was proposed to eliminate the major cusp plane associated with most cusp mirror systems (U.S. Pat. No. 4,007,392). This structure also had the advantages of a nearly spherical symmetry to the confinement field, and the generation of a minimum B field at the center. The structure did still have the center of the individual mirrors as loss vectors. Contrasting to the simple mirror approach is the field reversed mirror approach, in which some of the inner magnetic field lines close back on themselves, creating a region in which plasma is more efficiently trapped. Confinement should improve since trapped particles must diffuse across the closed field lines before they can escape through a mirror. The more prominent approaches include the Astron scheme, field reversed ion rings formed by cusp injection, field reversed theta pinch, and the adiabatic compression of plasma gun injected vortices. A more recent method produces a field-reversed plasma ring by a coaxial plasma gun, and confines the ring into the minimum B-field of a magnetic mirror (U.S. Pat. No. 4,314,879).
More recent attempts at confinement have centered on the toroidal approach. One proposed solution for the drift problem of toroidal confinement was the Stellarator, where helical windings provided shear and rotational transforms. In one case, a single winding is in the form of a figure eight. The drift motion in this field can be minimized by the particles repeated motion through the confinement region, making one loop near the outer edge, which would then become the other half of the figure eight and be near the inner surface of the structure. Poloidal coils have been added to toroidal windings to address sheer, as well as containment coils with windings in layers with different pitch, creating a "high shear" configuration. The tokamak approach has a toroidal magnetic field supplemented by a poloidal component produced by a large current in the plasma itself. Multiple cusp mirrors as the interior walls (U.S. Pat. No. 4,233,537) and pinch coils to better produce a concave field (U.S. Pat. No. 3,523,206) have been tried. The multipole approach has their magnetic field entirely or primarily in the poloidal direction. The typical multipole has four rings defining the inner, outer, top, and bottom edges of a torus. The current can be carried in the same direction, so that there is a minimum B field in the center region. The current can also be carried in alternating opposite directions, forming a linear cusp between each adjacent pair of coils. This linear cusp suffers from plasma losses like any cusp-mirror, in this case along the cusp line. An approach to reduce losses from most forms of line cusps and point cusps was to place reflector fields along the cusp loss regions (U.S. Pat. No. 4,430,290). The very recent work has centered on refinements of the toroidal approach, with no real new schemes being offered.
A thorough review of the history of magnetic fusion research at Lawrence Livermore Laboratory is found in the May 1978 issue of Energy and Technology Review Lawrence Livermore Laboratory, encompassing the major approaches in magnetic mirror confinement. A general overview of the physics of magnetic confinement of plasma can be found in Francis F. Chen's Introduction of Plasma Physics, published by Plenum Press, New York, 1974, with chapter nine being devoted to the problems associated with controlled nuclear fusion, including discussion of the advantages and disadvantages of all major approaches that have been attempted.
Technical References Cited:
______________________________________ U.S. Pat. Nos. 3,170,841 1965 Post 3,369,140 1968 Furth 3,461,033 1969 Michel 3,491,318 1970 Henning 3,523,206 1970 Drabrer 3,582,849 1971 Post 3,668,067 1972 Christofilos 3,728,217 1973 Dandl 4,007,392 1977 Valfells 4,233,537 1980 Limpaecher 4,314,879 1982 Hartman 4,430,290 1984 Kiryu ______________________________________
Energy and Technology Review, May 1978, Lawrence Livermore Laboratory
Introduction to Plasma Physics, chapter 9, Plenum Press, NY, 1974, Francis F. Chen